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864

Appendix IL

be investigated, as examples of slider-crank  and quadriocrank
chains respectively.

Fig. 826 is the linkwork of an oscillating engine, where CP is
the crank and BP the piston rod, and the ratio w of CP to wj. of
B P is required. Linear velocity of P, normally to c P = #, and
normally to B P = v^ Now if i) = s P, v-^=s T, and

sr

^ = — =

x           T5T>

BP

ST
B P

But by similar triangles

ST
SP

sr   v

B P   S P

BP
OP

BP    #
—. —

BP   OP

Again,

Produce
Also draw-

d v = wj • o P

z> = w x rad. = a) • c P

6U - CP = o^ -OP

B p to F, and draw G F at right angles to B F.
G F || c P, making triangles B F G, B p c similar.

>      OP     BP     B c

~ = — = — = —

>!       C P       P F        C G

or, if B c be angular velocity of crank, c G- is that of piston rod
Then, if c G be turned round to g, a point is found in a polar
curve of angular velocity of B p when w is constant.

In the quadric crank, Fig. 827, let o be the virtual centre.
Then w. A P = zi, and o^ B Q = \. Draw AL || B Q, making
triangles o P Q and A P L similar. Also produce Q P to s, making
triangles SAL and SBQ similar.

Finally

o> • AP

or

v

AP

OP
1 OQ
•BQ

A P • AL

_ AP
AL

.BQ
" AI,

BS

A~S

If the chain be that of a beam engine, w is constant and
represented by B Q, while ^ is shewn by A L. Turn A L round on
to line A p and a point I is found in a polar curve which shews
uj-i for any position of crank A p.

P.502. Efficiency of Transruissian by Shafting,— The